Table Of ContentAutomaticAlgorithm RecognitionandReplacement
ANewApproachtoProgramOptimization
RobertMetzgerandZhaofangWen
TheMITPress
Cambridge,Massachusetts
London,England
(cid:2)c 2000MassachusettsInstituteofTechnology
Allrightsreserved.Nopartofthisbookmaybereproducedinanyformbyanyelectronicormechanicalmeans
(includingphotocopying,recording,orinformationstorageandretrieval)withoutpermissioninwritingfromthe
publisher.
ThisbookwassetinTimesRomanbytheauthorusingtheLATEXdocumentpreparationsystem.
PrintedonrecycledpaperandboundintheUnitedStatesofAmerica.
LibraryofCongressCataloging-in-PublicationData
Metzger,RobertC.Automaticalgorithmrecognitionandreplacement:anew
approachtoprogramoptimization /RobertMetzger, ZhaofangWen. p.
cm.
Includesbibliographicalreferencesandindex.
ISBN0-262-13386-7(alk.paper)
1.Computeralgorithms.2.Computerprogramming.I.Wen,Zhaofang.II.
Title.
QA76.9.A43M482000
005.1–dc21
99-088044
Contents
ListofFigures v
ListofTables ix
Acknowledgments xi
1 Introduction 1
2 TheProblemandItsComplexity 15
3 RelatedWork 31
4 ReducingProgramVariation 51
5 InternalProgramRepresentation 69
6 ConvertingtoaCanonicalForm 87
7 MatchingSubprogramsandPatterns 117
8 ExtractingSubprograms 129
9 ValidAlgorithmReplacement 137
10 SelectingAlgorithmReplacements 145
11 PerformingAlgorithmReplacements 153
12 TimeComplexityandPerformance 161
13 Conclusion 165
AppendixA:
SystemArchitecture 173
AppendixB:
ModuleDesign 179
AppendixC:
InputDefinition 191
AppendixD:
StatisticsonHeuristicBehavior 203
References 209
Index 213
ListofFigures
1.1 QRTriangularization—triangularizationphase 5
1.2 QRTriangularization—constructionofQphase 6
2.1 Algorithmicallyequivalentloops 20
2.2 I-valsoriginateinseveralways 21
2.3 Type expressionsforFortranvariablesINTEGER M,Nand
REALA(100),B(*),C(M,N) 22
2.4 TypeexpressionsforCvariablesintM,N,A[],*B,**C,*D[100] 23
2.5 Algorithmicinstance 24
2.6 Parenthesesoperatorandalgorithmicinstances 25
2.7 Multiplevariablerolesandalgorithmicinstances 25
2.8 Constraintconsistencyinalgorithmicinstancetesting 26
2.9 Typeconsistencyinalgorithmicinstancetesting 27
4.1 Controlflownormalization—beforeandafter 53
4.2 Inductionvariablestrengthreduction—beforeandafter 53
4.3 Scalarexpansion—beforeandafter 54
4.4 Reductivescalartemporaryremoval—beforeandafter 56
4.5 Procedurecallinlining—beforeandafter 57
4.6 Loopdistribution—before 57
4.7 Loopdistribution—after 58
4.8 Conditionaldistribution—beforeandafter 59
4.9 Looppermutation—beforeandafter 59
4.10 Commonsubexpressionelimination—beforeandafter 60
4.11 Redundantassignmentelimination—beforeandafter 61
4.12 Unreachablecodeelimination—beforeandafter 62
4.13 Loopinvariantmotion—beforeandafter 63
4.14 Looprerolling—beforeandafter 64
4.15 Constantpropagation—beforeandafter 67
4.16 Algebraicsimplification 68
5.1 Representationofanarrayelement 70
vi ListofFigures
5.2 Assignmentstatementinloop 70
5.3 Representationofanassignmentstatement 71
5.4 PointerandarraysarerelatedinC 71
5.5 Theinternalrepresentationofp[15]and*(p+15)forC 72
5.6 Notationsusedintheconstructdiagrams 73
5.7 Acontrol-groupliststhestatementsexecutedunderthesame
condition 73
5.8 Thecounter-loopconstructisusedtorepresentFortrandoloops 73
5.9 Thepre-test-loopconstructisusedtorepresentCwhileloops 74
5.10 Thepost-test-loopconstructisusedtorepresentCdo-whileloops 74
5.11 Theif-thenconstructisusedrepresentanif-thenstatement 75
5.12 Theif-then-elseconstructisusedtorepresentanif-then-else
statement 75
5.13 ConstructsrepresentingAssignmentandI/Ostatements 75
5.14 Constructs representing C return, continue, and break
statements 76
5.15 Thecallconstructisusedtorepresentalibraryprocedurecall 76
5.16 Typeconstructs 77
5.17 Thegrammarfori-valrepresentation 78
5.18 Asubtreerepresentingani-val 78
5.19 Ani-valsubtree 79
5.20 Constructingthestatement-leveldataflowdependencegraphs 81
5.21 Matrixmultiplyexample 81
5.22 Binarysearchexample 82
5.23 Thecontroltreeandthevariable-leveldataflowdependence
graphforamatrixmultiplysubroutine 83
5.24 Thecontroltreeandthevariable-leveldataflowdependence
graphforabinarysearchfunction 84
6.1 Isomorphicexpressiontrees 89
6.2 Non-isomorphicexpressiontrees 90
6.3 Algorithmtoperformtreeorientation 94
ListofFigures vii
6.4 Algorithmtoperformlexicographicsortofstrings 95
6.5 Twoexpressiontrees 95
6.6 Difficultcasesfordistinguishingvariablesbycontext 96
6.7 Algorithmtoperforminitialencoding 97
6.8 Algorithmtorefineencoding 101
6.9 Algorithmtosplitgroupsbyinstancetrees 102
6.10 StepsofprocedureSplitGroupByInstanceTrees,part1 103
6.11 StepsofprocedureSplitGroupByInstanceTrees,part2 104
6.12 Algorithmtosplitgroupsbydistancegraphs 105
6.13 StepsofprocedureSplitGroupByDistanceGraph,part1 106
6.14 StepsofprocedureSplitGroupByDistanceGraph,part2 107
6.15 Algorithmtosplitgroupsbypathstoroot 108
6.16 StepsofprocedureSplitGroupByPathsToRoot,part1 109
6.17 StepsofprocedureSplitGroupByPathsToRoot,part2 110
6.18 Algorithmtoupdatecodesaftersplittinggroups 111
6.19 Algorithmtoadjustcontrolgroups 113
6.20 Algorithmtoperformprioritizedtopologicalsort 114
6.21 Ani-valtree 116
7.1 Algorithmtomatchcontroltrees 118
7.2 Bandedmatrixloop—patternsubprogram 119
7.3 Bandedmatrixloop—extractedsubprogram 119
7.4 I-valtreesforthepatternsubprogram 120
7.5 I-valtreesfortheextractedsubprogram 120
7.6 Anexampleofthepatterndatabaseindexstructure 126
8.1 Computationallyconfluentcode 130
8.2 Algorithmtoextractsubprogramsformatching 132
8.3 Algorithmtofindallconnectedinducedsubgraphvertexsets 134
9.1 Collapsingverticesofadirectedacyclicgraphmayintroduce
directedcycles 138
9.2 Non-overlappingreplacementscode 140
viii ListofFigures
9.3 Algorithmtodeterminethefeasibilityofreplacements 142
10.1 Algorithmfindingselectionthatmaximizesreplacementbenefit 150
11.1 Algorithmtoperformalgorithmreplacements 154
11.2 Subprogrambeforeandafterreplacement 156
11.3 Thecontroltreebeforeandafteralgorithmreplacement 157
12.1 Algorithmrecognitionandreplacementsystemflowchart 162
A.1 Algorithmrecognitionandreplacementsystemarchitecture 175
A.2 Algorithmrecognitionprototypedataflow 177
B.1 Structurechartforalgorithmrecognitionandreplacement 179
B.2 Structurechartformatchinganextractedsubprogramagainst
thepatterns 182
B.3 Structurechartforpreprocessingapattern 187
ListofTables
D.1 Initialpatterngroups 204
D.2 Distributionofgroupswithinvariantset1 205
D.3 Distributionofgroupswithinvariantset2 206
D.4 Distributionofgroupswithinvariantset3 206
D.5 Distributionofcontrolgroupsizes 207
x ListofTables
Acknowledgments
ThisworkwaspartiallysponsoredbytheAirForceMaterialCommandandtheAdvanced
Research Projects Agency / CSTO, under ARPA Order No. B548, issued by ESC/ENS
underContract#F19628-94-C-0058.TheremainderoftheworkwasfundedbytheConvex
Division of the Hewlett-PackardCompany,formerlyConvexComputer Corporation.We
thankbothARPAandConvex/HPforallowingustoundertakethisproject.
WenwouldliketoexpresshisappreciationtoTerryCaracuzzo,MarkSchroeder,and
RobertCoxforsharingtheirvaluablein-depthexperiencesoftheConvexoptimizingcom-
piler. He also enjoyedmany interestingconversationswith Terry Caracuzzoon compiler
optimizationsthatnotonlyhelpedthe implementationsof ourpreprocessingtransforma-
tions, but also sharpened the ideas of the system design. He thanks Derek G. Corneil
for pointing out the best algorithms on graph isomorphism. He would also like to thank
StephanOlariuforstimulatingdiscussionsonalgorithmsdesignandforpointingoutref-
erencesingraphtheoryrelatedtothisproject.HeisverygratefultoC.MikeOverstreetfor
firstintroducinghimtothefieldofprogramanalysisandtransformation.
PresleySmithandSteveWallachencouragedMetzgertoseekexternalfundingforhis
research ideas. He thanks them for their support and confidence in his efforts. Randall
MercerwrotethefirstpatternmatchingtransformationsintheConvexvectorizingFortran
compiler,whicheventuallyconvincedMetzgerofthevalueoftheconceptandtheimpos-
sibilityoftheapproach.
GregAstfalkandJoelWilliamsonfoundnumerousmistakesinourfirstdraftandsug-
gestedcorrectionsonbothformandcontent.Wethankthembothfortheirdiligentefforts.
AugustinDubrulleprovidedtheQRtriangularizationexampleintheintroductorychapter.
SeanStroudandMatthewDiazhelpedusresurrecttheConvexApplicationCompilerfor
useinpreprocessingapplicationcodes.
Weacknowledgethecommentsoftheanonymousreferees,whichhelpedusimprove
the textin severalways, as well as the help of our editor at MIT Press, Doug Sery, who
helpedusnavigatetheseeminglyinterminablepathfromdrafttobook.
Anyerrorsthatremainarepurelytheresponsibilityoftheauthors.
